consider have a metric [itex]ds^2=f(r,t)dt^2+g(r,t)dr^2+k(r,t)dΩ^2[/itex] if g(r,t) =0, we have black hole? any metric that has this condition, are black hole? or not this is first clue to determine black hole and we should check some other features! solution of g(r,t)=0, may have some roots, for example BTZ black hole has two horizon, what we can interpret two horizon? for example,BTZ has inner and outer horizon! what's this mean? what happen between two horizon?